Mrs Miller has written to the chairman of the BBC Trust, Lord Patten, to stress that the corporation's investigations into itself should be conducted "thoroughly".

In his response, Lord Patten said Mrs Miller knows "how seriously the trust takes the allegations", and added the inquiries would be "comprehensive and independent".

"Some of these cases have been passed to the police where appropriate, and we are reviewing others within our normal HR processes and procedures," it said in a statement.

In a two-hour appearance before the committee, Mr Entwistle said a "broader cultural problem" at the BBC in the past had allowed the abuse by Savile, who regularly appeared on British TV in the 1960s, 70s and 80s.

A number of key issues were raised during the director general's grilling.

He said he had been told about the Newsnight probe while he was head of BBC Vision, but added he did not press for more details as he did not want to show "undue interest" in a news issue

He insisted Newsnight editor Peter Rippon had decided to drop the Savile investigation "on his own account" and there was "no external pressure"

Conservative MP Philip Davies told Mr Entwistle he needed to "get a grip" on his organisation, after he failed to tell them how many allegations of sexual harassment had been made against BBC employees past and present

'Gravely serious matter'

Mr Entwistle told MPs: "There is no question that what Jimmy Savile did and the way the BBC behaved in the years - the culture and practices of the BBC seems to allow Jimmy Savile to do what he did - will raise questions of trust for us and reputation for us.

"This is a gravely serious matter and one cannot look back at it with anything other than horror, frankly, that... his activities went on as long as they did undetected."

Police have launched a criminal investigation into Savile, who died last year aged 84.

They have described him as a predatory sex offender and believe he may have abused many people - including young girls - over a 40-year period.

On Monday, the BBC's Panorama programme reported on the abuse allegations against Savile as well as the decision by Newsnight last December to drop its investigations into the claims.

"I came away from Panorama firmly of the view that that investigation, even if in the judgement of the editor it wasn't ready for transmission at the point he was looking at it, should have been allowed to continue," Mr Entwistle said.

Asked whether there had been pressure from management on Newsnight to drop its Savile investigation, he said there was no evidence of this and denied any BBC cover-up of the allegations.

He said Peter Rippon had become convinced that examining whether police had failed properly to investigate Savile was crucial to airing the Newsnight report.

BBC home editor Mark Easton said Mr Entwistle portrayed an "almost baffling" system at the BBC.

"He talks about the situation where the head of television felt unable to talk to the head of news about an investigation which might have a direct impact on his Christmas schedules.

"I think people will find it very odd that you have what he called the 'referring up' structure - you don't have a refer across - so you have to go a long way up to come back down again.

"And that can make the BBC - I think people in the corporation would agree - sometimes a bit flat-footed. Outside people might say it makes them look a bit daft."

After Mr Entwistle made his appearance, Channel 4 News said it had obtained an email written by Liz MacKean - the Newsnight reporter responsible for the investigation - claiming Mr Rippon tried to "kill" her story with "impossible editorial demands".

Ms MacKean wrote to a friend to say her editor had told her Savile's alleged victims "were teenagers, not too young... they weren't the worst kind of sexual offences."

A BBC spokesman said "it would not be appropriate to comment" on Ms MacKean's email until a review by former head of Sky News, Nick Pollard, had concluded.

In his blog earlier this month defending his decision to pull the probe, Mr Rippon said he was "guided by editorial considerations only", adding some of the team "disagreed strongly with [his] judgement" while others "agreed equally strongly".

Mr Entwistle said he had asked Mr Rippon to step aside because of inaccuracies in the blog.

But he said that he believed, "to the best of the evidence we have been able to assemble", the explanation now being offered for the dropping of the Newsnight report was accurate.

An independent inquiry led by former Sky head of news Nick Pollard will examine whether there were any failings in the BBC's management of the Newsnight investigation.

Christmas schedule

Mr Entwistle was asked about a brief conversation with BBC director of news Helen Boaden last December about the possibility of Newsnight running their report about Savile, while Mr Entwistle, as then BBC director of Vision, was planning Christmas tribute pieces to the presenter.

Savile died in October 2011 aged 84 having previously denied allegations he was a paedophile

"The key message I took away was that it wasn't yet clear to Helen whether it was going to stand up or not," he said.

"I wouldn't have had any qualms about making any changes we needed to make to the Christmas schedule."

Asked whether he now regretted running the tribute programmes for Savile, Mr Entwistle told MPs: "In the light of what's happening, of course I do."

He added that the Panorama programme pointed to the BBC's health as a media organisation, rather than being a "symptom of chaos", because it showed the organisation's capacity to investigate itself.

He said no other news organisation in the world would do this.

Later Mr Entwistle emailed BBC staff to pledge the corporation was "determined to be open and transparent, however painful it may feel at times"

He added: "It is only by opening ourselves up that we can restore and maintain the trust of our audiences."

On Monday, former Court of Appeal judge Dame Janet Smith will begin a review into the culture and practices of the BBC during Savile's time at the corporation and will also examine if the BBC's child protection and whistleblowing policies are fit for purpose.

Jimmy Savile was a man with a high profile public persona, built on decades of broadcasting and charitable work.

He was seen as a flamboyant eccentric but is now accused of years of sexual abuse.

Culture secretary Mrs Miller wrote to Lord Patten: "We have talked about the paramount importance of full public trust in the BBC's inquiries and agreed that it is essential that licence fee payers can be assured that they are being conducted thoroughly and with the full co-operation of the BBC."

Lord Patten replied: "You have recognised both the credibility and the scope of those who are leading the inquiries and the wide scope of their terms of reference."

But he issued a warning that the government should not wade into the row: "I know that you will not want to give any impression that you are questioning the independence of the BBC," he said.